The systems and methods described herein include hexapod systems, Stewart platform systems and other mechanical movement systems, in which a set of independently moveable trucks support legs that couple to a working surface capable of holding a machine tool or other end-effector, and preferably wherein the trucks travel across a reference surface, such as around the circumference of a circle or along some other pre-defined geometrical pattern or track. For example, as described herein, the systems include Stewart platform machines that have six supportive legs each of which connects to a truck that can travel independently along a track. By coordinating the movement of these six trucks, the working surface can be moved in three dimensional space and can be oriented about three axes, providing control of roll, pitch and yaw.